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In this study, we investigate the performance of several nonlinear filters for noise reduction in image signals. We find that the total variation (TV) regularization filter exhibits the best performance for effective noise reduction and picture quality preservation. We analyze the behavior of the TV regularization filter and elucidate how noise is reduced effectively without losing edge sharpness...
This paper focuses on residual analysis of statistical independence of multiple variables from the viewpoint of linear algebra. The results show that multidimensional residuals are represented as linear sum of determinants of 2 × 2 submatrices, which can be viewed as information granules measuring the degree of statistical dependence.
One of the most important problems in data mining is how to manage a large amount of data and to extract efficient knowledge from large databases. Although many machine learning methods and statistical methods have been proposed to solve this problem, they are not powerful when we have more than 1000 samples, since the computational complexity of these algorithms is larger than or approximately equal...
This paper shows the meaning of Pearson residuals as an indicator of statistical independence in a multi-way contingency table. While information granules of statistical independence of two variables can be viewed as determinants of 2 ?? 2- submatrices, those of multivariate cases consist of linear sum of residuals for odds ratios, which can be viewed as an extention of determinants in 2 ?? 2 matrices.
Background: Recent neurophysiological studies have evaluated neural synchronization using wavelet transformation and the phase-locking factor (PLF). However, mathematical details of PLF and statistical processes to examine the significance of PLF have remained unclear. The present report discusses the significance level of PLF. Methods: Mathematization of PLF was performed, and results for PLF simulation...
This paper focuses on statistical independence of multiple variables from the viewpoint of linear algebra. The residual for odds ratio, which can be viewed as an extension of the determinant of two dimensional contingency matrix, plays an important role in decomposition of multivariate data tables.
This paper focuses on statistical independence of multiple variables from the viewpoint of linear algebra. While information granules of statistical independence of two variables can be viewed as determinants of 2 times 2- submatrices, those of three variables consist of several combination s of determinants. However, this combination can be viewed as a linear sum over the all combinarial pairs of...
The class-D audio amplifier using delta-sigma(DeltaSigma) modulation technique has been spotlighted recently. In order to obtain a high performance class-D amplifier, the order of the DeltaSigma modulator needs to be higher as much as possible. However the design of high-order DeltaSigma modulator is very difficult because of necessity of optimal parameter setting with keeping system stability. In...
This paper shows the meaning of Pearson residuals as an indicator of statistical independence. While information granules of statistical independence of two variables can be viewed as determinants of 2times2-submatrices, those of three variables consist of several combinations of linear equations which will become residuals for odds ratio (outer products) when they are equal to 0. Interestingly, the...
This paper focuses on statistical independence of more than three variables from the viewpoint of linear algebra. While information granules of statistical independence of two variables can be viewed as determinants of 2 times 2- submatrices, those of three variables consist of several combination s of odds ratios, which can be viewed as a multivariate extension of determinants. Thus, in a more than...
In this paper, we present a method for clustering asymmetric proximity data. First, we calculate the indiscernibility level for each object pair, that quantifies the level of global agreement for regarding the two objects as indiscernible. Then, hierarchical linkage grouping is applied to unite objects according to the derived indiscernibility level. This scheme enables users to examine the hierarchy...
This paper shows the meaning of Pearson residuals when a contingency table is three dimensional. While information granules of statistical independence of two variables can be viewed as determinants of 2 times 2- submatrices, those of three variables consist of several combinations of linear equations which will become odds ratio when they are equal to 0. Interstingly, the property on the symmetry...
This paper focuses on how statistical independence can be observed in a contingency table when the table is viewed as a matrix. Statistical independence in a contingency table is represented as a special form of linear dependence, where all the rows or columns are described by one row or column, respectively. This also means that the rank of the matrix is equal to 1.0. When the rank is equal to 1,...
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